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Register a new userImproving Linear State-Space Models with Additional Iterations
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An estimated state-space model can possibly be improved by further iterations with estimation data. This contribution specifically studies if models obtained by subspace estimation can be improved by subsequent re-estimation of the B, C, and D matrices (which involves linear estimation problems). Several tests are performed, which shows that it is generally advisable to do such further re-estimation steps using the maximum likelihood criterion. Stated more succinctly in terms of MATLAB functions, ssest generally outperforms n4sid.
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This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM), which is found useful in solving sophisticated event-based state estimation problems. An indirect modeling approach is developed, wherein a state space model (SSM) is firstly identified for a Gaussian system and the SSM is then used as an emulator for learning an HMM. In the proposed method, the training data for the HMM are obtained from the data generated by the SSM through building a quantization mapping. Parameter learning algorithms are designed to learn the parameters of the HMM, through exploiting the periodical structural characteristics of the HMM. The convergence and asymptotic properties of the proposed algorithms are analyzed. The HMM learned using the proposed algorithms is applied to event-triggered state estimation, and numerical results on model learning and state estimation demonstrate the validity of the proposed algorithms.
This paper presents a dynamic state observer design for discrete-time linear time-varying systems that robustly achieves equalized recovery despite delayed or missing observations, where the set of all temporal patterns for the missing or delayed data is modeled by a finite-length language. By introducing a mapping of the language onto a reduced event-based language, we design a state estimator that adapts based on the history of available data at each step, and satisfies equalized recovery for all patterns in the reduced language. In contrast to existing equalized recovery estimators, the proposed design considers the equalized recovery level as a decision variable, which enables us to directly obtain the global minimum for the intermediate recovery level, resulting in improved estimation performance. Finally, we demonstrate the effectiveness of the proposed observer when compared to existing approaches using several illustrative examples.
This paper discusses linearized models of hydropower plants (HPPs). First, it reviews state-of-the-art models and discusses their non-linearities, then it proposes suitable linearization strategies for the plant head, discharge, and turbine torque. It is shown that neglecting the dependency of the hydroacoustic resistance on the discharge leads to a linear formulation of the hydraulic circuits model. For the turbine, a numerical linearization based on a first-order Taylor expansion is proposed. Model performance is evaluated for a medium- and a low-head HPP with a Francis and Kaplan turbine, respectively. Perspective applications of these linear models are in the context of efficient model predictive control of HPPs based on convex optimization.
Risk-sensitive safety analysis is a safety analysis method for stochastic systems on Borel spaces that uses a risk functional from finance called Conditional Value-at-Risk (CVaR). CVaR provides a particularly expressive way to quantify the safety of a control system, as it represents the average cost in a fraction of worst cases. In prior work, the notion of a risk-sensitive safe set was defined in terms of a non-standard optimal control problem, in which a maximum cost is assessed via CVaR. Here, we provide a method to compute risk-sensitive safe sets exactly in principle by utilizing a state-space augmentation technique. In addition, we prove the existence of an optimal pre-commitment policy under a measurable selection condition. The proposed framework assumes continuous system dynamics and cost functions, but is otherwise flexible. In particular, it can accommodate probabilistic control policies, fairly general disturbance distributions, and control-dependent, non-monotonic, and non-convex stage costs. We demonstrate how risk-sensitive safety analysis is useful for a stormwater infrastructure application. Our numerical examples are inspired by current challenges that cities face in managing precipitation uncertainty.
We present a method for incremental modeling and time-varying control of unknown nonlinear systems. The method combines elements of evolving intelligence, granular machine learning, and multi-variable control. We propose a State-Space Fuzzy-set-Based evolving Modeling (SS-FBeM) approach. The resulting fuzzy model is structurally and parametrically developed from a data stream with focus on memory and data coverage. The fuzzy controller also evolves, based on the data instances and fuzzy model parameters. Its local gains are redesigned in real-time -- whenever the corresponding local fuzzy models change -- from the solution of a linear matrix inequality problem derived from a fuzzy Lyapunov function and bounded input conditions. We have shown one-step prediction and asymptotic stabilization of the Henon chaos.
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